Trying to make it matter.
[Textbook School Math] gives students (and teachers) a gimmick; the CCSMS require that students actually learn mathematics.
I agree with his basic premise that the CCSS are superior to our current set, but his treatment of the proof of (-1)(-1)=1 as a Common Core strategy is almost laughable. I'm not so sure that my average algebra student would find that as anything more than mathematical sleight of hand that still doesn't satisfy their curiosity about what a negative times a negative actually means. However, until I get published in a leading educational journal I should probably keep my mouth shut. :-)
I think the point Wu's trying to make about the treatment of (-1)(-1)=1 is that the follow-the-pattern method amounts do an inductive gimmick. I'll admit I've used the pattern method, but I agree with him. Having students explore different ways to find an answer to (-1)(-1 + 1) may be sufficient for helping them make the appropriate connections.
I agree with you on both accounts...I've also used the pattern method with exponents to show that anything to the zero power is one and that's just as gimmicky (I think) but I'm not sure how to teach it otherwise (I have used the division of bases = subtraction of exponents property and that seems to work... Or let the students find that one) . I'm not sure how to go about letting the students dive into it with just the right amount of direction since I've never tried but I'm not sure that any student would come up with his answer which is just as gimmicky of a proof, in my opinion. Explaining what it really means is a whole other story and one that I feel un equipped to tell.
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